TY - JOUR
AU - L. Miao
AU - Zh. Pu
PY - 2011/11/25
Y2 - 2024/03/04
TI - <i>Q</i> -permutable subgroups of finite groups
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 63
IS - 11
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2823
AB - A subgroup $H$ of a group $G$ is called $Q$-permutable in $G$ if there exists a subgroup $B$ of $G$ such that (1) $G = HB$ and (2) if $H_1$ is a maximal subgroup of $H$ containing $H_{QG}$, then $H_1B = BH_1 < G$, where $H_{QG}$ is the largest permutable subgroup of $G$ contained in $H$. In this paper we prove that: Let $F$ be a saturated formation containing $U$ and $G$ be a group with a normal subgroup $H$ such that $G/H \in F$. If every maximal subgroup of every noncyclic Sylow subgroup of $F∗(H)$ having no supersolvable supplement in $G$is $Q$-permutable in $G$, then $G \in F$.
ER -